Engineering Entrance Exam Question and Answers | Relations and Functions - Zigya

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11.

The number of real roots of equation loge(x) + ex = 0 is

  • 0

  • 1

  • 2

  • 3


12.

Let the number of elements of the sets A and B be p and q, respectively. Then, the number of relations from the set A to the set B is

  • 2p + q

  • 2pq

  • p + q

  • pq


13.

Eleven apples are distributed among a girl and a boy, Then, which one of the following statements is true ?

  • atleast one of them will receive 7 apples

  • the girl receives atleast 4 apples or the boy receives atleast 9 apples

  • the girl receives atleast 5 apples or the boy receives atleast 8 apples

  • the girl receives atleast 4 apples or the boy receives atleast 8 apples


14.

The domain of definition of the function

fx = 1 + loge1 - x

  • -  < x  0

  • -  < x  e - 1e

  • -  < x  1

  • x  1 - e


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15.

The function f(x) = log1 + x1 - x satisfies the equation

  • f(x + 2) - 2f(x + 1) + f(x) = 0

  • f(x) + f(x + 1) = f{x(x + 1)}

  • f(x) + f(y) = fx + y1 + xy

  • f(x + y) = f(x)f(y)


16.

The range of the function f (x) = loge4 - x2 is given by

  • 0, 

  • - , 

  • - , loge2

  • loge2, 


17.

If log5log5log2x = 0, then the value of x is

  • 32

  • 125

  • 625

  • 25


18.

A mapping f : N ➔ N, where N is the set of natural numbers is defined as

f(n) = n2 for n odd

f(n) = 2n + 1, for n even

for n ∈ N. Then f is

  • surjective but not injective

  • injective but not surjective

  • bijective

  • neither injective nor surjective


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19.

A function f: A  B, where A = {x: - 1  x  1} and B = {y: 1  y  2} is defined by the rule y = f(x) = 1 + x2 Which of the following statement is true ?

  • f is injective but not surjective

  • f is surjective but not injective

  • f is both injective and surjective

  • f is neither injective nor surjective


20.

The equation ex - x - 1 = 0 has, apart from x = 0

  • one other real root

  • two real roots

  • no other real root

  • infinite number of real roots


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